1. **Stating the problem:** Graph the system of inequalities $$\begin{cases} y \geq x + 2 \\ y \leq x - 3 \end{cases}$$ 2. **Understanding the inequalities:** - The first inequality $y \geq x + 2$ represents the region above or on the line $y = x + 2$. - The second inequality $y \leq x - 3$ represents the region below or on the line $y = x - 3$. 3. **Check the lines:** - Both lines have the same slope $m=1$, so they are parallel. - The line $y = x + 2$ is shifted 5 units above $y = x - 3$. 4. **Analyze the system:** - Since the first inequality requires $y$ to be greater than or equal to $x + 2$ (above the upper line), - and the second requires $y$ to be less than or equal to $x - 3$ (below the lower line), - there is no overlap between these regions because the upper boundary is always above the lower boundary. 5. **Conclusion:** - The system has no solution because the shaded regions do not intersect. **Final answer:** The system $$\begin{cases} y \geq x + 2 \\ y \leq x - 3 \end{cases}$$ has no solution; the feasible region is empty.